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Bounds on the volume of the physical universe

Jeff Cheeger proved for a compact manifold $\lambda_1 \le 1/4 Cg(X)^2$ where $Cg(X) = \inf_S Area(S)/min(Vol(A),Vol(B))$ where $S$ runs over hypersurfaces cutting $X$ into two parts.  Buser showed a lower bound $lambda_1 \ge a Cg(X) + b Cg(X)^2$.  We can use these to produce bounds on the volume of the universe, which is a hypersurface of $S^4(1/h)$ where we know $lambda_1 = 4 h$.  Such bounds are conservative but nontrivial.